Kinds Of Mappings Research Articles

New soft operators related to supra soft $ \delta_i $-open sets and applications

<abstract><p>This project aimed to introduce the notion of supra soft $ \delta_i $-open sets in supra soft topological spaces. Also, we declared the differences between the new concept and other old generalizations. We presented new operators such as supra soft $ \delta_i $-interior, supra soft $ \delta_i $-closure, supra soft $ \delta_i $-boundary and supra soft $ \delta_i $-cluster. We found out many deviations to our new operators; to name a few: If $ int^s_{\delta_i}(F, E) = (F, E) $, then it doesn't imply that $ (F, E) \in SOS_{\delta_i}(X) $. Furthermore, we applied this notion to define new kinds of mappings, like supra soft $ \delta_i $-continuous mappings, supra soft $ \delta_i $-irresolute mappings, supra soft $ \delta_i $-open mappings and supra soft $ \delta_i $-closed mappings. We studied their main properties in special to distinguish between our new notions and the previous generalizations. It has been pointed out in this work that many famous previous studies have been investigated here; in fact, I believe that this is an extra justification for the work included in this manuscript.</p></abstract>

Existence of best proximity points for the sum of two operators

In this paper, we work on the existence of approximate solution for the fixed point equation Rx + Qx = x, when R is a weak contractive mapping and Q is a continuous self-map which is a new topic related to the background literature. Till now, no results were found to find the existence of approximate solution for such a kind of mappings in literature to the best of our knowledge. Here we prove the existence of best proximity point for the sum of a weak contractive non self map and a continuous self map. Also, we provide an example to support our main theorem. And also, we prove the existence of best proximity point for the sum of Geraghty-contraction and continuous map.

Metrizable subspaces of representation spaces

We show that various representation spaces for continua contain a homeomorphic copy of the harmonic sequence, so even though it is not a T0 space, it contains infinite metrizable subspaces. It remains an open question whether this representation space (topologized using continuous surjections) contains a closed subspace homeomorphic to the harmonic sequence. In fact, the representation space for continua topologized using various kinds of mappings (open, confluent, or monotone mappings, for instance) can be shown to have some closed points, but it remains open in many cases whether there are more than two closed points in most instances. Examples of closed points include the pseudo-arc and the universal pseudo-solenoid. Along the way, we find a few related results about metrizable subspaces of representation spaces for continua.

Best Proximity Point Theorems without Fuzzy P-Property for Several (ψ − ϕ)-Weak Contractions in Non-Archimedean Fuzzy Metric Spaces

This paper addresses a problem of global optimization in a non-Archimedean fuzzy metric space context without fuzzy P-property. Specifically, it concerns the determination of the fuzzy distance between two subsets of a non-Archimedean fuzzy metric space. Our approach to solving this problem is to find an optimal approximate solution to a fixed point equation. This approach has been well studied within a category of problems called proximity point problems. We explore some new types of (ψ−ϕ)-weak proximal contractions and investigate the existence of the unique best proximity point for such kinds of mappings. Subsequently, some fixed point results for corresponding contractions are proved, and some illustrative examples are presented to support the validity of the main results. Moreover, an interesting application in computer science, particularly in the domain of words has been provided. Our work is a fuzzy generalization of the proximity point problem by means of fuzzy fixed point method.

Existence and Convergence of Fixed points of Generalized alpha non-expensive mappings in metric spaces

We give certain conditions about different kinds of mappings. These conditions willbe median of non-expansive mappings and quasi-non-expansive mappings. We will establish somefixed point results of some generalized non-expansive mappings in metric spaces. Moreover, wewill also establish few existence and convergence results about generalization of non-expansivemappings. Finally, we present some useful lemmas and propositions.

New results of three different kinds of mappings based on fuzzifying semi-θ-neighborhood system

In this article, we will define the new notions (e.g., semi-θ-neighbor-hood system of point, semi-θ-closure (interior) of a set and semi-θ-closed (open) set) based on fuzzy logic (i.e., fuzzifying topology). Then, we will explain the interesting properties of above five notions in detail. Several basic results (for instance, Definition 2.3, Theorem 2.5 (iii), (v) and (vi), Theorem 2.10, Theorem 2.14 and Theorem 4.6) in classical topology are generalized to the fuzzy case based on Łukasiewicz logic. In addition to, we will show that every fuzzifying semi-θ-closed set is fuzzifying semi-closed set (by Theorem 2.5 (vi)). Further, we will study the notion of fuzzifying semi-θ-derived set and fuzzifying semi-θ-boundary set, and discuss several of their fundamental basic relations and properties. Also, we will present a new type of fuzzifying strongly semi-θ-continuous mapping between two fuzzifying topological spaces. Finally, several characterizations of fuzzifying strongly semi-θ-continuous mapping, fuzzifying strongly semi-θ-irresolute mapping, and fuzzifying weakly semi-θ-irresolute mapping along with different conditions for their existence are obtained.

A fixed point principle in ordered metric spaces and applications to rational type contractions

<abstract><p>Fixed points results for rational type contractions in metric spaces have been widely studied in the literature. In the last years, many of these results are obtained in the context of partially ordered metric spaces. In this paper, we introduce a fixed point principle for a class of mappings between partially ordered metric spaces that we call orbitally order continuous. We show that the hypotheses in the statement of such a principle are not redundant and, in addition, that they cannot be weakened in order to guarantee the existence of a fixed point. Moreover, the relationship between this kind of mappings and those that are continuous and orbitally continuous is discussed. As an application, we extend many fixed point theorems for continuous contractions of rational type to the framework of those that are only orbitally order continuous. Furthermore, we get extensions of the aforementioned metric fixed point results to the framework of partial metrics. This is achieved thanks to the fact that each partial metric induces in a natural way a metric in such a way that our new principle is applicable. In both approaches, the metric and the partial metric, we show that there are orbitally order continuous mappings that satisfy all assumptions in our new fixed point principle but that they are not contractions of rational type. The explored theory is illustrated by means of appropriate examples.</p></abstract>

$ \acute{C} $iri$ \acute{c} $-Reich-Rus type weakly contractive mappings and related fixed point results in modular-like spaces with application

<abstract><p>In this article, we define a new space named the modular-like space with its related concepts to prove the existence of a fixed point and a point of coincidence for mappings on this space. Also, we defined $ \acute{C} $iri$ \acute{c} $-Reich-Rus type weakly contractive mappings on modular-like spaces and discussed some conditions that guarantee the existence of the fixed points for these kind of mappings. Some examples are also provided to elaborate the usability of our main results. It is worth mentioning that a modular-like space is a generalization of a modular space, thus our theorems are more general and applicable than the fixed point theorems on modular spaces.</p></abstract>

Existence of fixed points of weak enriched nonexpansive mappings in Banach spaces

In this work, we introduce and study a new class of weak enriched nonexpasive mappings which is a generalization of enriched nonexpansive mappings provided by Berinde [Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces], Carpathian J. Math., 35 (2019), No. 3, 293–304]. This class of mappings generalizes several important classes of nonlinear mappings. We prove some fixed point theorems regarding this kind of mappings which extend some important results in [Berinde, V., Approximating fixed points of enriched nonexpansive mappings by Krasnoselskij iteration in Hilbert spaces, Carpathian J. Math., 35 (2019), No. 3, 293–304]. Moreover, some examples, to ensure the existence of these mappings and support our main theorems, are also given.

More on Selective Covering Properties in Bitopological Spaces

In this study, we continue our investigation of selective covering properties in bitopological spaces. We discuss their behaviour under certain kinds of mappings. We also introduce selective versions of the ccc property and the star-ccc property in bitopological spaces and give few of their relations with other selective properties. Also, we consider preservation of selective covering properties of bitopological spaces under some known relations in bitopological context.

Best proximity points of (EP)-operators with qualitative analysis and simulation

In this paper, we analyze a Thakur three-step iterative process adapted for the context of non-self-mappings. Based on this iteration, we state and prove the existence of best proximity points for the recently introduced class of (EP)-non-self-mappings. Under certain assumptions, we study the convergence of the considered Thakur process to a best proximity point for the same class of operators. Moreover, we design a CQ-type algorithm which strongly converges to a best proximity point of such kind of mappings. In addition, we present the CQ-variant of the proposed algorithm that strongly converges to a best proximity pair. Some examples and numerical simulations sustain the efficiency of our new algorithms.

Almost and weakly NSR, NSM and NSH spaces

In this paper we introduce and study some new types of star-selection principles (almost and weakly neighbourhood star-Menger, neighbourhood star-Rothberger and neighbourhood star-Hurewicz). We establish some properties of these selection principles and their relations with other selection properties of topological spaces. Behaviour of these classes of spaces under certain kinds of mappings is also considered.

Towards online myoelectric control based on muscle synergies-to-force mapping for robotic applications

The development of a functional myoelectric control represents a big challenge within the researchers community, due to the complexity of mapping the user’s movement intention onto the control signals. It is continuously gaining attention since it could be useful for building natural, intuitive and tailored human–machine interfaces. In this context, muscle synergies-based approaches are playing an important role since they may be useful to exploit the modular organization of the musculoskeletal system.Muscle synergies-based myo-control schemes have shown promising results when they are trained and validated at the same limb pose. However, dealing with a muscle-to-force mapping variability across multiple limb poses remains an open challenge, thus keeping these techniques unusable in several real application scenarios, e.g. rehabilitation contexts.In this paper, the authors propose a method able to compute the synergies-to-force mapping of a new limb pose by interpolation, with the knowledge of the synergies-to-force mapping related to a limited set of limb poses. The proposed interpolation-based approach has been evaluated on three different kind of mappings: muscle-to-force, “Pose-Shared” synergies-to-force and “Pose-Related” synergies-to-force. The muscle-to-force mapping considers a direct map between muscles and hand force. Both synergies-to-force approaches consider a map between muscle synergies and hand force, but, the “Pose-Shared” mapping assumes that the muscle patterns can be factorized using data coming from different limb poses, whereas the “Pose-Related” one assumes that each pose has its own set of muscle primitives that can be clustered together. The generalization capability of the proposed approach has been evaluated by comparing performances obtained in untrained conditions with the ones obtained in trained upper limb poses. Results showed that synergies-based approach substantially reduce the performance loss when tested on untrained upper-limb’s poses, demonstrating that muscle synergies may be suitable to be shared across different working conditions. Moreover, the feasibility of the proposed approach has been preliminary tested in an online condition, demonstrating that the subject was able to accomplish the force task by controlling a virtual cursor with his muscular activations.

On Integral Inequalities Involving Generalized Lipschitzian Functions

A new class of mappings that includes the class of Lipschitzian mappings is introduced. For this kind of mappings, new integral inequalities of Hadamard’s type are obtained. Our results are extensions of many previous contributions related to integral inequalities for Lipschitzian mappings.

New fixed point results for F-contractions of Hardy–Rogers type in b-metric spaces with applications

The purpose of this paper is to introduce the notions of extended F-contraction of Hardy–Rogers type, extended F-contraction of Suzuki–Hardy–Rogers type and generalized F-weak contraction of Hardy–Rogers type and to establish some new fixed point results for such kind of mappings in the setting of complete b-metric spaces. These fixed point results improve (and/or) extend those obtained in Vetro (Nonlinear Anal Model Control 21(4):531–546, 2016) and Lukacs and Kajanto (Fixed Point Theory 19(1):321–334, 2018) since some conditions made therein are removed or weakened. In addition, some illustrative examples are provided to show the usability of the obtained results. As an application of our results, we obtain the existence and uniqueness of solutions for certain functional, integral and differential equations.

Mappings and Connectedness on Hesitant Fuzzy Soft Multispaces

In this paper, we introduce the concept of mapping on hesitant fuzzy soft multisets and present some results for this type of mappings. The notions of inverse image and identity mapping are defined, and their basic properties are investigated. Hence, kinds of mappings and the composition of two hesitant fuzzy soft multimapping with the same dimension are presented. The concept of hesitant fuzzy soft multitopology is defined, and certain types of hesitant fuzzy soft multimapping such as continuity, open, closed, and homeomorphism are presented in detail. Also, their properties and results are studied. In addition, the concept of hesitant fuzzy soft multiconnected spaces is introduced.

Reassessing truth-evaluability in the Minimalism-Contextualism debate

The debate between Semantic Minimalism and Radical Contextualism is standardly characterized as concerning truth-evaluability—specifically, whether or not sentences require rich contextualization in order to express complete, truth-evaluable contents. In this paper, I examine the notion of truth-evaluability, considering which kinds of mappings it might require from worldly states of affairs to truth-values. At one end of the spectrum, an exhaustive notion would require truth-evaluable contents to map all possible states of affairs to truth-values. At the other end, a liberal notion would require only that truth-evaluable contents map at least one possible state of affairs to at least one truth-value. I show that both Minimalists and Radical Contextualists rely on some intermediate, moderately strict notion of truth-evaluability, falling between these two poles. I consider four ways in which such a notion could be defined. However, I argue that each of these is ultimately implausible, giving us no reason to favour a moderately strict notion of truth-evaluability over the liberal alternative. This suggests that the debate must shift to more moderate ground; rather than concerning the in principle possibility of truth-evaluable contents, it fundamentally hinges on their explanatory value. More generally, paying close attention to the notion of truth-evaluability allows us to tease apart distinct strands in the Minimalism-Contextualism debate, and gain a better appreciation of what is at stake.

Non-Archimedean fuzzy metric spaces and Best proximity point theorems

In this paper, we introduce some new classes of proximal contraction mappings and establish best proximity point theorems for such kinds of mappings in a non-Archimedean fuzzy metric space. As consequences of these results, we deduce certain new best proximity and fixed point theorems in partially ordered non-Archimedean fuzzy metric spaces. Moreover, we present an example to illustrate the usability of the obtained results.

A New Class of Contraction inb-Metric Spaces and Applications

A novel class ofα-β-contraction for a pair of mappings is introduced in the setting ofb-metric spaces. Existence and uniqueness of coincidence and common fixed points for such kind of mappings are investigated. Results are supported with relevant examples. At the end, results are applied to find the solution of an integral equation.

On the lower order of mappings with finite length distortion

We study the problem of the so-called lower order for one kind of mappings with finite distortion, actively investigated in the recent 15–20 years.We prove that mappings with finite length distortion f: D → ℝn, n ≥ 2, whose outer dilatation is integrable to the power α > n − 1 with finite asymptotic limit have lower order bounded from below.